This article investigates a propellant-free transfer between Lissa jous orbits in the Sun-Earth system modelled as a photo-gravitational circular restricted three body p roblem. The geometry of the phase space around the L 1 , 2 equilibrium points is exploited to change the amplitudes and phases of the initial Lissajous orbit using the associated hyperbolic invarian t manifolds. The desired Lissajous orbit is reached by cancelling out the instabilities by means o f solar radiation pressure manoeuvres. The acceleration required is controlled by the change in the spacecraft’s reflectivity and angle of incidence of the Sun-line direction. Changes in reflectivit y allow transfers along the x -axis, while re-orientations of the spacecraft move the equilibrium p oints, and the orbits around them, towards the x - y plane. For equilibrium points in the x - y plane, the in-plane centre manifold tends to a center × centre × focus equilibrium. The analytical solution is extended to this general case. An analysis in the magnitude of the manoeuvre required is pres ented for different Lissajous orbit amplitudes and reflectivity, along with a comment on harnessing solar radiation pressure devices